MADRID—
Bernard Esnoult
had just booked a flight from Lyon, France, to Vienna when an email from the online travel agency he had used landed in his inbox.

“Dear Bernard,” it said. “You have tried to reserve a flight at Opodo.fr. If you wish to benefit from the best prices, we invite you to finish your reservation now.” Believing his booking had failed, Mr. Esnoult said he clicked a bar labeled “Finish your reservation” and typed his bank details a second time.

Weeks later, he said, he learned that he had been double-billed by Opodo. “This is how I was scammed,” said the 65-year-old Frenchman, adding that he had called and emailed Opodo for two weeks in November until his bank intervened to help annul the second billing. Opodo denied trying to mislead Mr. Esnoult.

Opodo.fr is one of 67 websites run by
eDreams Odigeo SA,
a Barcelona company that has grown to rival Expedia Inc. at the top of the market in airline bookings.

A Wall Street Journal review of complaints against the company found indications of irregularities in dozens of cases. Some involved billing twice for a single ticket or concealing additional costs in advertised prices—practices lawyers say would violate European Union consumer-protection laws. The review, based on interviews and documents provided by Odigeo customers, found that many had waited months for the return of ticket payments that were canceled or paid for twice, or were charged premium rates for calls to Odigeo’s customer-service line.

Odigeo denies breaking any laws. A spokesman said its prices contain no hidden surcharges, and any double bookings are the result of customer errors or technical faults in Odigeo’s system or those of the airlines. Odigeo’s booking notification, he said, gives “clear information regarding any additional action that may be required from the customer.”

Less than 1% of the millions of tickets Odigeo sold in 43 countries last year drew customer complaints, he said.

Dozens of online travel agencies offer nearly identical services, and search engines such as Google Inc., which drive traffic to online travel agents, are expanding into the market themselves. The squeeze on the industry has Odigeo and rival agencies scrambling for extra dollars from customers, said Martin Alcock, director of the London-based Travel Trade Consultancy.

“It’s a balancing act,” Mr. Alcock said, “pushing as much as you can while making sure you are not breaking any consumer laws.”

Odigeo has had troubles with finances and customers. It cut its earnings forecast shortly after being listed on Spain’s stock exchange last April, and it has since lost nearly 80% of its value. On Monday, its founder and chief executive, Javier Pérez-Tenessa de Block, resigned, saying new leadership was needed after a year of poor results. Dana Dunne, elevated from chief operating officer to replace him, said one priority is to “improve our level of service and product offering.”

The company is a conspicuous target on Facebook, TripAdvisor and forums such as 60 Millions de Consommateurs, a state-funded French magazine that reviews consumer products. The magazine said more than half the roughly 300 reader complaints about travel agencies sent to it last year involved Odigeo’s sites. France is Odigeo’s largest single market.

TripAdvisor, a leading travel-review site, has since June 2013 carried a warning against using any Odigeo site. François Aubert, a former travel agent who acts as an unpaid air-travel expert on TripAdvisor, said complaints about Odigeo were different from those about Expedia. Travelers use words such as “scam” and “to avoid” in describing experiences with Odigeo, said Mr. Aubert, who wrote the TripAdvisor warning. “We see a lot of complaints on Expedia too,” he added, “but I don’t see much on them where customers feel betrayed.”

Asked to comment, an Odigeo spokesman said the company takes customer service “very seriously” and is increasing its investment in that area.

Founded with the name eDreams in 1999, the company grew into a leading booker in Spain and Italy as consumers reserved more tickets over the Internet.

In 2010, U.K. buyout firm Permira purchased a majority stake. A year later, eDreams led a merger with French agency Go Voyages and U.K.-based Opodo, creating Odigeo. Along the way, the company assumed more than €450 million ($511 million) in debts.

As competition grew, the company advertised tickets priced low enough to appear first on price-comparison sites such as Kayak.com. The strategy drove traffic to its sites but customers complained.

Air France took Odigeo to court in 2011, saying the agency had violated EU and French regulations by adding service fees as customers went through the booking process. Odigeo said the allegations were unfounded and settled out of court. Two years later Air France alleged breach of settlement, seeking $13.1 million in damages. The two are negotiating a new settlement, Odigeo said.

Dutch, Italian, French and U.K. government agencies have cited similar concerns. British Airways and Iberia briefly blocked three Odigeo websites from selling their tickets in October. The airlines said they lifted the ban after Odigeo complied with EU price-transparency regulations. Odigeo said the core of the dispute was over commercial terms, not price transparency, an assertion the airlines denied.

Moody’s Investors Service lowered its outlook for Odigeo’s debt ratings to negative in December, saying the airlines’ ban had illustrated the industry’s business risks. Moody’s said that while Odigeo’s liquidity was “adequate,” that could change if revenue kept declining.

Travel companies hold customers’ money for weeks and earn interest on it before paying airlines for the customers’ tickets. The money passing through Odigeo is 10 times its revenue, Mr. Pérez-Tenessa, the outgoing CEO, said in October. The company said its “optimization” of cash management boosted working capital by €18 million in the third quarter.

A French group that mediates in customer disputes with Odigeo said it has handled hundreds of complaints of refund delays, double-billings and unjustified surcharges. “Mistakes can happen, but we are seeing cases with a remarkable similarity on a daily basis,” said Monique Rongieras, a retired civil servant who organized the group through Facebook in 2013.

The Odigeo spokesman said the average time to process a refund is 3½ working days, but in several cases reviewed by the Journal, Odigeo told customers in emails that refunds generally take two to 12 weeks.

Some have taken even longer. Paul Neill, an operations director at a U.K. fitness-equipment company, said he spent 16 weeks calling and emailing Opodo to demand a promised refund after canceling a flight to Las Vegas last June. He said he got the money back only after his credit-card company disputed the charge. Odigeo said Mr. Neill’s case was a “unique situation” because it depended on payment from a third party before the company could refund him.

European statutes don’t make it clear how long a travel company can legally withhold a refund. But a spokesman for the Civil Aviation Authority, the U.K. enforcement body for air travel, said months-long delays are “unacceptable.”

“I wonder how many people just give up on getting a refund,” Mr. Neill said.